Question

5.
A rhombus shaped field has green grass for 18 cows to graze. If each side of the
rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each
cow be getting?​

Answer 1

Let the field be ABCD

GIVEN:

The side of Rhombus is 30m.

Therefore,AB=BC=CD=AD=30m.

And also the diagonal is 48m.

That is BD=48m.

AREA OF RHOMBUS=AREA OF ∆ABD+AREA OF ∆BCD

∆ABD;

AREA OF ∆=√s(s-a)(s-b)(s-c) sq.units

Here,s is the semi perimeter,and a,b,c are sides of traingles.

Here,

(AD)a=30m,

(AB)b=30m,

(BD)c=48m,

S=a+b+c/2 OR Perimeter/2

=30+30+48/2

=108/2

=54m

Giving the values of a=30m;b=30m;c=48m & s=54m

AREA OF ∆ABD

=√s(s-a)(s-b)(s-c) sq.units

=√54(54-30)(54-30)(54-48)

=√54(24)(24)(6)

=24√54×6

=24√(9×6)×6

=24×6×3

=432m²

Hence,

The AREA OF ∆ABD=432m²

Similarly,

The AREA OF ∆BCD=432m².....[as both of the traingles has the same sides(length)]

Therefore,

AREA OF RHOMBUS

=AREA OF ∆ABD+AREA OF ∆BCD

=432m²+432m²

=864m²

It is given that 18 cows to graze the field.

So,

AREA FOR 18COWS

=AREA OF RHOMBUS

=864m²

AREA OF EACH COW

=AREA OF RHOMBUS/18

=864/18

=48m²

Thus,each cow will graze 48m² area of the grass field..